Four identical spheres each of mass M and radius 10 cm, each are placed on a horizontal surface touching one another so that their centres are located at the corners of a square of side 20 cm. What is the distance of their centre of mass from centre of any of the spheres?

Options

A. 5 cm
B. 10 cm
C. 20 cm
D. `10 sqrt2 cm`

Answer

D

Explanation

`x_(CM)=(Mxx0+Mxx20+Mxx20+M+0)/(4M)=10 cm`
Similarly, `y_(CM) =10 cm`
Hence, distance of centre of mass from centre of any one sphere, say
`r=sqrt((10-0)^2+(10-0)^2)=10sqrt2cm`